Multiply the following complex numbers, marked as blue dots on the graph: $( e^{\pi i / 4}) \cdot (7)$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $ e^{\pi i / 4}$ ) has angle $\frac{1}{4}\pi$ and radius $1$ The second number ( $7$ ) has angle $0$ and radius $7$ The radius of the result will be $1 \cdot 7$ , which is $7$ The angle of the result is $\frac{1}{4}\pi + 0 = \frac{1}{4}\pi$ The radius of the result is $7$ and the angle of the result is $\frac{1}{4}\pi$.